xaby a≠0, b>0,b≠1, xєR

Exponential Growth Exponential Decay

(0,a) (0,a)

b > 1, b = _______________

a = __________________

H. Asymptote: y = ______

0 < b < 1, b = _______________

a = _________________

H. Asymptote : y = ______

growth factor decay factor

y-intercept on parent fcn y-intercept on parent fcn

0 0

NOTES DAY 8.1

XX YY

-2-2 2/92/9

-1-1 2/32/3

00 22

11 66The “b” is NOT the

y-intercept in an exponential function

· 3

· 3

· 3

+1

+1

+1

“a” is the starting point and b is the product from one y-value to the next

Y = 2 · 3x

XX YY

-2-2 125125

-1-1 2525

00 55

11 11

· 1/5

· 1/5

· 1/5

+1

+1

+1

The “a” is the starting point and so a = 5

y = 5 · (1/5)xThe b is the product, so b = 1/5

Where a≠0 0<b<1

xaby

Causes a _________________ in the graph1a

10 a Causes a _________________ in the graph

0a Causes a _____________ in the x-axis

kaby hx

“h” causes a _______________________ in the graph

“k” causes a _______________________ in the graphVertical Translation

Vertical Shrink

Reflection

Horizontal Translation

Vertical Stretch

Parent:

Transformation:

Y = a(1+r)t

a = initial amount

r = growth rate

t = time period

1+r = growth factorIf the rate is 3% , then

The decay model is the same except

the decay factor is 1 – r

1.03 is the growth factor

You put $350 in a savings account that earns 3% annual interest compounded yearly. How much will that investment be worth in 4 years?

Y = a(1+r)t

Y = 350(1+0.03)4

Y ≈ $393.93 in 4 years

Complete a t-chart

Domain:Range:Y-intercept:

X Y

-2 3/4

-1 3/2

0 3

1 6

2 12(-∞,∞)(0,∞)(0,3)

Complete a t-chart

Domain:Range:H. Asymptote:

X Y

-2 9

-1 5

0 3

1 2

2 1.5(-∞,∞)(1,∞)Y=1

Equation: xy )3(2400

322 4

1

xx

44

4

1

322

xx

2)3(22 xx

9622 2 xxx

780 2 xx

}7,1{x

X=7

1. 2. 3x = 27 3. 32X-1=27 X+2x2

8

1

x22 3

3x

333 x

3x

)2(3

33 )12(

x

x

6312 xx

x 7

Activity: Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer.

HW : WS 8.1

A. x = 0B. y = 0C. x = 2D. y = 2

A. Y = 3x+1 + 3B. Y = 3x-1 + 3C. Y = 3x+3 + 1D. y = 3x-3 +1

A. Y = 3x+1 + 3B. Y = 3x-1 + 3C. Y = 3x+3 + 1D. y = 3x-3 + 1

A. Translated up 1 unitB. Translated down 1 unitC. Reflected over the x-axisD. Reflected over the y-axis

A. y=2(3)x

B. y=3(2)x

C. Y=2x3

D. y=3x2

A. y=50(3)5

B. y=50(1.03)5

C. Y=3(50)5

D. y=1.03(50)5

A. 2x+2=81/3B. 32x+2 =34

C. 9x+2 = 81D. 32x+2 = 92

A. X = X-4B. 3x =3-2X+8

C. 3x = (32)X-4

D. X = 2X-4

A. X-5 = 1B. 4x-5 = 43

C. 4x-5 = 4-3

D. X-5 = 64